Place the turkey breast on a sheet tray and rub with the 1 tablespoon olive oil, 1 ½ teaspoon salt, ½ teaspoon pepper, 2 teaspoons rosemary, 2 teaspoons thyme. Roast the turkey for about 1 hour and 5 minutes, or until the internal temperature reaches 165 degrees.
Remove from the oven and let rest. After it’s rested for 15–20 minutes, lightly shred the turkey with two forks to produce large strands of turkey.
In a saucepan, heat the remaining olive oil. Add the remaining salt and pepper, garlic, remaining rosemary, and remaining thyme and let simmer for 2 minutes. Stir in milk and bring to a simmer. Let simmer for 2–3 minutes, then pour into a pasta serving bowl.
Bring a large pot of salted water to boil, then cook the linguine according to the package instructions.
A couple minutes before the pasta is done, whisk the sour cream into the milk sauce. Once the pasta is done cooking, drain it and add it to the sauce, along with the turkey. Toss the pasta all together until completely coated in sauce. Garnish with grated Parmesan and extra herbs, if desired.